What is the solution for (dy)/(dx)=((x^2+1))/(e^y) ?

The solution for (dy)/(dx)=((x^2+1))/(e^y) is y=ln((x^3)/3+x+c_{1})

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(dy)/(dx)=((x^2+1))/(e^y)

\frac{d y}{d x} = \frac{( x ^{2} + 1 )}{e ^{y}}

y = ln (\frac{x ^{3}}{3} + x + c_{1})

Solution steps

\frac{d y}{d x} = \frac{( x ^{2} + 1 )}{e ^{y}}

Solve separable ODE:

y = ln (\frac{x ^{3}}{3} + x + c_{1})

y = ln (\frac{x ^{3}}{3} + x + c_{1})

\int (\frac{x ^{2}}{1 - x ^{2}}) d x

2 t cos (t)

- y d x + (x + x y) d y = 0

x \to - 8 + lim (\frac{x + 9}{x + 8})

f (x) = x^{2} - 2 x, at x = - 2

What is the solution for (dy)/(dx)=((x^2+1))/(e^y) ?
The solution for (dy)/(dx)=((x^2+1))/(e^y) is y=ln((x^3)/3+x+c_{1})